New constructions of CSS codes obtained by moving to higher alphabets

Iryna Andriyanova (1) , Denise Maurice (2) , Jean-Pierre Tillich (2)

1 ETIS - UMR 8051 - Equipes Traitement de l'Information et Systèmes
2 SECRET - Security, Cryptology and Transmissions

We generalize a construction of non-binary quantum LDPC codes over $\F_{2^m}$ due to \cite{KHIS11a} and apply it in particular to toric codes. We obtain in this way not only codes with better rates than toric codes but also improve dramatically the performance of standard iterative decoding. Moreover, the new codes obtained in this fashion inherit the distance properties of the underlying toric codes and have therefore a minimum distance which grows as the square root of the length of the code for fixed $m$.

Domaines: Théorie de l'information et codage [math.IT]; Théorie de l'information [cs.IT]; Physique Quantique [quant-ph]

Iryna Andriyanova, Denise Maurice, Jean-Pierre Tillich. New constructions of CSS codes obtained by moving to higher alphabets. 2012. ⟨hal-00671659⟩